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Volumn 13, Issue 3, 2003, Pages 812-823

Traveling fronts in an array of coupled symmetric bistable units

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EID: 0141678064     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1586511     Document Type: Article
Times cited : (8)

References (48)
  • 1
    • 12044252828 scopus 로고
    • Pattern formation outside of equilibrium
    • M.C. Cross and P.C. Hohenberg, "Pattern formation outside of equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993); C. Bowman and A.C. Newell, "Natural patterns and wavelets," ibid. 70, 289-301 (1998).
    • (1993) Rev. Mod. Phys. , vol.65 , pp. 851-1112
    • Cross, M.C.1    Hohenberg, P.C.2
  • 2
    • 0039835170 scopus 로고    scopus 로고
    • Natural patterns and wavelets
    • M.C. Cross and P.C. Hohenberg, "Pattern formation outside of equilibrium," Rev. Mod. Phys. 65, 851-1112 (1993); C. Bowman and A.C. Newell, "Natural patterns and wavelets," ibid. 70, 289-301 (1998).
    • (1998) Rev. Mod. Phys. , vol.70 , pp. 289-301
    • Bowman, C.1    Newell, A.C.2
  • 7
    • 0000638990 scopus 로고
    • Optical memory and spatial chaos
    • W.J. Firth, "Optical memory and spatial chaos," Phys. Rev. Lett. 61, 329-332 (1988).
    • (1988) Phys. Rev. Lett. , vol.61 , pp. 329-332
    • Firth, W.J.1
  • 8
    • 0000234351 scopus 로고
    • Propagation failure in arrays of coupled bistable chemical oscillators
    • J.P. Laplante and T. Erneux, "Propagation failure in arrays of coupled bistable chemical oscillators," J. Phys. Chem. 96, 4931-4934 (1992).
    • (1992) J. Phys. Chem. , vol.96 , pp. 4931-4934
    • Laplante, J.P.1    Erneux, T.2
  • 9
    • 0000688571 scopus 로고
    • Nagumo's equation
    • H.P. McKean, "Nagumo's equation," Adv. Math. 4, 209-223 (1970).
    • (1970) Adv. Math. , vol.4 , pp. 209-223
    • McKean, H.P.1
  • 10
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • R. FitzHugh, "Impulses and physiological states in theoretical models of nerve membrane," Biophys. J. 1, 445-466 (1961).
    • (1961) Biophys. J. , vol.1 , pp. 445-466
    • Fitzhugh, R.1
  • 11
    • 0023362335 scopus 로고
    • Propagation and its failure in coupled systems of discrete excitable cells
    • J.P. Keener, "Propagation and its failure in coupled systems of discrete excitable cells," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 47, 556572 (1987).
    • (1987) SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. , vol.47 , pp. 556-572
    • Keener, J.P.1
  • 12
    • 43949163245 scopus 로고
    • Propagating waves in discrete bistable reaction-diffusion systems
    • T. Erneux and G. Nicolis, "Propagating waves in discrete bistable reaction-diffusion systems," Physica D 67, 237-244 (1993).
    • (1993) Physica D , vol.67 , pp. 237-244
    • Erneux, T.1    Nicolis, G.2
  • 15
    • 58149208726 scopus 로고
    • Multistability in networks of weakly coupled bistable units
    • R.S. MacKay and J.-A. Sepulchre, "Multistability in networks of weakly coupled bistable units," Physica D 82, 243-254 (1995).
    • (1995) Physica D , vol.82 , pp. 243-254
    • MacKay, R.S.1    Sepulchre, J.-A.2
  • 16
    • 0000440983 scopus 로고    scopus 로고
    • Universal scaling of wave propagation failure in arrays of coupled nonlinear cells
    • K. Kladko, I. Mitkov, and A.R. Bishop, "Universal scaling of wave propagation failure in arrays of coupled nonlinear cells," Phys. Rev. Lett. 84, 4505-4508 (2000).
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 4505-4508
    • Kladko, K.1    Mitkov, I.2    Bishop, A.R.3
  • 17
    • 0035948026 scopus 로고    scopus 로고
    • Wave front depinning transition in discrete one-dimensional reaction-diffusion systems
    • A. Carpio and L.L. Bonilla, "Wave front depinning transition in discrete one-dimensional reaction-diffusion systems," Phys. Rev. Lett. 86, 6034-6037 (2001).
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 6034-6037
    • Carpio, A.1    Bonilla, L.L.2
  • 18
    • 0020191444 scopus 로고
    • Propagation phenomena in a bistable reaction-diffusion system
    • J. Rinzel and D. Terman, "Propagation phenomena in a bistable reaction-diffusion system," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 42, 1111-1137 (1982).
    • (1982) SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. , vol.42 , pp. 1111-1137
    • Rinzel, J.1    Terman, D.2
  • 19
    • 0000653552 scopus 로고
    • Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems
    • H. Ikeda, M. Mimura, and Y. Nishiura, "Global bifurcation phenomena of travelling wave solutions for some bistable reaction-diffusion systems, " Nonlinear Anal. Theory, Methods Appl. 13, 507-526 (1989).
    • (1989) Nonlinear Anal. Theory, Methods Appl. , vol.13 , pp. 507-526
    • Ikeda, H.1    Mimura, M.2    Nishiura, Y.3
  • 20
    • 0000085224 scopus 로고
    • Pattern formation in non-gradient reaction-diffusion systems: The effects of front bifurcations
    • A. Hagberg and E. Meron, "Pattern formation in non-gradient reaction-diffusion systems: The effects of front bifurcations," Nonlinearity 7, 805-835 (1994); "Complex pattern in reaction-diffusion systems: A tale of two front instabilities," Chaos 4, 477-484 (1994).
    • (1994) Nonlinearity , vol.7 , pp. 805-835
    • Hagberg, A.1    Meron, E.2
  • 21
    • 0041111359 scopus 로고
    • Complex pattern in reaction-diffusion systems: A tale of two front instabilities
    • A. Hagberg and E. Meron, "Pattern formation in non-gradient reaction-diffusion systems: The effects of front bifurcations," Nonlinearity 7, 805-835 (1994); "Complex pattern in reaction-diffusion systems: A tale of two front instabilities," Chaos 4, 477-484 (1994).
    • (1994) Chaos , vol.4 , pp. 477-484
  • 23
    • 0035682535 scopus 로고    scopus 로고
    • Onset of wave fronts in a discrete bistable medium
    • D. Pazó and V. Pérez-Muñuzuri, "Onset of wave fronts in a discrete bistable medium," Phys. Rev. E 64, 065203(R) (2001).
    • (2001) Phys. Rev. E , vol.64
    • Pazó, D.1    Pérez-Muñuzuri, V.2
  • 24
    • 0000077902 scopus 로고    scopus 로고
    • Propagation failure of travelling waves in a discrete bistable medium
    • G. Fáth, "Propagation failure of travelling waves in a discrete bistable medium," Physica D 116, 176-190 (1998).
    • (1998) Physica D , vol.116 , pp. 176-190
    • Fáth, G.1
  • 25
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • E.N. Lorenz, "Deterministic nonperiodic flow," J. Atmos. Sci. 20, 130-141 (1963).
    • (1963) J. Atmos. Sci. , vol.20 , pp. 130-141
    • Lorenz, E.N.1
  • 27
    • 0034226841 scopus 로고    scopus 로고
    • Dynamics of three-tori in a periodically forced Navier-Stokes flow
    • J.M. Lopez and F. Marques, "Dynamics of three-tori in a periodically forced Navier-Stokes flow," Phys. Rev. Lett. 85, 972-975 (2000).
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 972-975
    • Lopez, J.M.1    Marques, F.2
  • 28
    • 0000025107 scopus 로고
    • Homoclinic phenomena in optothermal bistability with localized absorption
    • J.I. Rosell, J. Farjas, R. Herrero, F. Pi, and G. Orriols, "Homoclinic phenomena in optothermal bistability with localized absorption," Physica D 85, 509-547 (1995); R. Herrero, J. Farjas, R. Pons, F. Pi, and G. Orriols, "Gluing bifurcations in optothermal devices," Phys. Rev. E 57, 5366-5377 (1998).
    • (1995) Physica D , vol.85 , pp. 509-547
    • Rosell, J.I.1    Farjas, J.2    Herrero, R.3    Pi, F.4    Orriols, G.5
  • 29
    • 0032075163 scopus 로고    scopus 로고
    • Gluing bifurcations in optothermal devices
    • J.I. Rosell, J. Farjas, R. Herrero, F. Pi, and G. Orriols, "Homoclinic phenomena in optothermal bistability with localized absorption," Physica D 85, 509-547 (1995); R. Herrero, J. Farjas, R. Pons, F. Pi, and G. Orriols, "Gluing bifurcations in optothermal devices," Phys. Rev. E 57, 5366-5377 (1998).
    • (1998) Phys. Rev. E , vol.57 , pp. 5366-5377
    • Herrero, R.1    Farjas, J.2    Pons, R.3    Pi, F.4    Orriols, G.5
  • 31
    • 84958286473 scopus 로고    scopus 로고
    • note
    • j. Nonetheless, we shall continue to work with ζ and η only, although keeping in mind that we are projecting the third variable.
  • 35
    • 0001234956 scopus 로고
    • A case of the existence of a denumerable set of periodic motions
    • L.P. Shil'nikov, "A case of the existence of a denumerable set of periodic motions," Sov. Math. Dokl. 6, 163-166 (1965).
    • (1965) Sov. Math. Dokl. , vol.6 , pp. 163-166
    • Shil'nikov, L.P.1
  • 36
    • 0021437639 scopus 로고
    • Local and global behavior near homoclinic orbits
    • P. Glendinning and C. Sparrow, "Local and global behavior near homoclinic orbits," J. Stat. Phys. 35, 645-696 (1984).
    • (1984) J. Stat. Phys. , vol.35 , pp. 645-696
    • Glendinning, P.1    Sparrow, C.2
  • 37
    • 84995270426 scopus 로고
    • A strange family of three-dimensional vector fields near a degenerate singularity
    • P. J. Holmes, "A strange family of three-dimensional vector fields near a degenerate singularity," J. Diff. Eqns. 37, 382-403 (1980).
    • (1980) J. Diff. Eqns. , vol.37 , pp. 382-403
    • Holmes, P.J.1
  • 38
    • 33846665703 scopus 로고
    • Bifurcations near homoclinic orbits with symmetry
    • P. Glendinning, "Bifurcations near homoclinic orbits with symmetry," Phys. Lett. A 103, 163-166 (1984).
    • (1984) Phys. Lett. A , vol.103 , pp. 163-166
    • Glendinning, P.1
  • 39
    • 0000755418 scopus 로고
    • Possible new strange attractors with spiral structure
    • A. Arneodo, P. Coullet, and C. Tresser, "Possible new strange attractors with spiral structure," Commun. Math. Phys. 79, 573-579 (1981).
    • (1981) Commun. Math. Phys. , vol.79 , pp. 573-579
    • Arneodo, A.1    Coullet, P.2    Tresser, C.3
  • 40
    • 0000980419 scopus 로고
    • On bifurcations of a homoclinic 'figure eight' for a saddle with a negative saddle value
    • D.V. Turaev and L.P. Shil'nikov, "On bifurcations of a homoclinic 'figure eight' for a saddle with a negative saddle value," Sov. Math. Dokl. 34, 397-401 (1987).
    • (1987) Sov. Math. Dokl. , vol.34 , pp. 397-401
    • Turaev, D.V.1    Shil'nikov, L.P.2
  • 42
    • 0000917836 scopus 로고
    • The gluing bifurcation I: Symbolic dynamics of the closed curves
    • J.M. Gambaudo, P. Glendinning, and C. Tresser, "The gluing bifurcation I: Symbolic dynamics of the closed curves," Nonlinearity 1, 203-214 (1988).
    • (1988) Nonlinearity , vol.1 , pp. 203-214
    • Gambaudo, J.M.1    Glendinning, P.2    Tresser, C.3
  • 45
    • 0034341441 scopus 로고    scopus 로고
    • Dynamics of a ring of diffusively coupled Lorenz oscillators
    • K. Josić and E. Wayne, "Dynamics of a ring of diffusively coupled Lorenz oscillators," J. Stat. Phys. 98, 1-30 (2000).
    • (2000) J. Stat. Phys. , vol.98 , pp. 1-30
    • Josić, K.1    Wayne, E.2
  • 46
    • 0035364394 scopus 로고    scopus 로고
    • Wave fronts and spatiotemporal chaos in an array of coupled Lorenz oscillators
    • D. Pazó, N. Montejo, and V. Pérez-Muñuzuri, "Wave fronts and spatiotemporal chaos in an array of coupled Lorenz oscillators," Phys. Rev. E 63, 066206 (2001).
    • (2001) Phys. Rev. E , vol.63 , pp. 066206
    • Pazó, D.1    Montejo, N.2    Pérez-Muñuzuri, V.3
  • 47
    • 0141428357 scopus 로고
    • Dynamical systems and models for reversals of the Earth's magnetic field
    • D.R.J. Chillingworth and R.J. Holmes, "Dynamical systems and models for reversals of the Earth's magnetic field," J. Int. Assoc. Math. Geol. 12, 41-59 (1980).
    • (1980) J. Int. Assoc. Math. Geol. , vol.12 , pp. 41-59
    • Chillingworth, D.R.J.1    Holmes, R.J.2


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